The Experts below are selected from a list of 121779 Experts worldwide ranked by ideXlab platform
K E Papadakis - One of the best experts on this subject based on the ideXlab platform.
-
orbit classification and networks of periodic orbits in the planar circular Restricted five body Problem
International Journal of Non-linear Mechanics, 2019Co-Authors: Euaggelos E Zotos, K E PapadakisAbstract:Abstract The aim of this paper is to numerically investigate the orbital dynamics of the circular planar Restricted Problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three main categories: (i) bounded (regular or chaotic) (ii) escaping and (iii) close encounter orbits. In addition, we determine the influence of the mass parameter on the orbital structure of the system, on the degree of fractality, as well as on the families of symmetric and non-symmetric periodic orbits. The networks and the linear stability of both symmetric and non-symmetric periodic orbits are revealed, while the corresponding critical periodic solutions are also identified. The parametric evolution of the horizontal and the vertical linear stability of the periodic orbits is also monitored, as a function of the mass parameter.
F Varadi - One of the best experts on this subject based on the ideXlab platform.
-
a study of orbits near saturn s triangular lagrangian points
Icarus, 1996Co-Authors: Colette M De La Barre, William M Kaula, F VaradiAbstract:Abstract We revisit the question whether orbits near Saturn's triangular Lagrangian points (L4 and L5) may be stable for the age of the Solar System. In this paper, asteroids potentially on these orbits are named “Bruins” for short. We numerically integrated orbits around the L4 and L5 Lagrangian points of Jupiter (Trojans) and Saturn: 40 Trojans and 350 Bruins, all of inclination less than 12°. Trojan orbits were numerically integrated along with Bruin orbits, so that by comparing the results, we might better understand Bruin orbital dynamics. Four Bruins were stable when the numerical integration was stopped at 412 Myrs. Properties of these stable orbits were: (1) proper eccentricities less than 0.028; (2) longitudes of perihelion that librate about a point 45° from Saturn's perihelion, such that the perihelia are never close when the Bruin's eccentricity is near maximum; (3) maximum eccentricities that do not occur when perihelia are near Jupiter's aphelion or when Jupiter is near its maximum eccentricity; and (4) libration angle about L4 or L5 of more than 80° (a measure of tadpole length). Orbits with libration angles less than 80° were unstable, the time to instability being correlated with libration angle. In contrast, long-lived Trojans may have very small tadpole orbits and longitudes of perihelion that either circulate or librate with respect to Jupiter's. We numerically integrated various Bruin orbits using different Solar System models to develop a Hamiltonian perturbation theory for low-inclination Bruin orbits. Although only at the beginning stages of development, the theory already identifies three separatrices of Bruin motion due in part to the Great Inequality (GI) between Jupiter and Saturn. These GI separatrices are a major contributor to the unstable region near Saturn's L4 and L5 points. We found a secular resonance between the perihelion precession rates of Saturn and a Bruin in the elliptic, Restricted Problem of three bodies with imposed motion of Saturn's perihelion. This resonance creates a separatrix of Bruin motion, which may cause low-inclination Bruins with circulating longitudes of perihelion to go unstable when Jupiter is added to the model. Although we still cannot say whether all Bruin orbits eventually go unstable, we can predict candidate stable orbits based on this work.
Euaggelos E Zotos - One of the best experts on this subject based on the ideXlab platform.
-
basins of convergence of equilibrium points in the Restricted three body Problem with modified gravitational potential
Chaos Solitons & Fractals, 2020Co-Authors: Euaggelos E Zotos, Wei Chen, Elbaz I AbouelmagdAbstract:Abstract This article aims to investigate the points of equilibrium and the associated convergence basins in the Restricted Problem with two primaries, with a modified gravitational potential. In particular, for one of the primary bodies, we add an external gravitational term of the form 1/r3, which is very common in general relativity and represents a gravitational field much stronger than the classical Newtonian one. Using the well-known Newton–Raphson iterator we numerically locate the position of the points of equilibrium, while we also obtain their linear stability. Furthermore, for the location of the points of equilibrium, we obtain semi-analytical functions of both the mass parameter and the transition parameter. Finally, we demonstrate how these two variable parameters affect the convergence dynamics of the system as well as the fractal degree of the basin diagrams. The fractal degree is derived by computing the (boundary) basin entropy.
-
orbit classification and networks of periodic orbits in the planar circular Restricted five body Problem
International Journal of Non-linear Mechanics, 2019Co-Authors: Euaggelos E Zotos, K E PapadakisAbstract:Abstract The aim of this paper is to numerically investigate the orbital dynamics of the circular planar Restricted Problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three main categories: (i) bounded (regular or chaotic) (ii) escaping and (iii) close encounter orbits. In addition, we determine the influence of the mass parameter on the orbital structure of the system, on the degree of fractality, as well as on the families of symmetric and non-symmetric periodic orbits. The networks and the linear stability of both symmetric and non-symmetric periodic orbits are revealed, while the corresponding critical periodic solutions are also identified. The parametric evolution of the horizontal and the vertical linear stability of the periodic orbits is also monitored, as a function of the mass parameter.
G Voyatzis - One of the best experts on this subject based on the ideXlab platform.
-
2 1 resonant periodic orbits in three dimensional planetary systems
Celestial Mechanics and Dynamical Astronomy, 2013Co-Authors: Kyriaki I Antoniadou, G VoyatzisAbstract:We consider the general spatial three body Problem and study the dynamics of planetary systems consisting of a star and two planets which evolve into 2/1 mean motion resonance and into inclined orbits. Our study is focused on the periodic orbits of the system given in a suitable rotating frame. The stability of periodic orbits characterize the evolution of any planetary system with initial conditions in their vicinity. Stable periodic orbits are associated with long term regular evolution, while unstable periodic orbits are surrounded by regions of chaotic motion. We compute many families of symmetric periodic orbits by applying two schemes of analytical continuation. In the first scheme, we start from the 2/1 (or 1/2) resonant periodic orbits of the Restricted Problem and in the second scheme, we start from vertical critical periodic orbits of the general planar Problem. Most of the periodic orbits are unstable, but many stable periodic orbits have been, also, found with mutual inclination up to 50◦–60◦, which may be related with the existence of real planetary systems.
-
on the 2 1 resonant planetary dynamics periodic orbits and dynamical stability
Monthly Notices of the Royal Astronomical Society, 2009Co-Authors: G Voyatzis, Thomas A Kotoulas, John D HadjidemetriouAbstract:The 2/1 resonant dynamics of a two-planet planar system is studied within the framework of the three-body Problem by computing families of periodic orbits and their linear stability. The continuation of resonant periodic orbits from the Restricted to the general Problem is studied in a systematic way. Starting from the Keplerian unperturbed system we obtain the resonant families of the circular Restricted Problem. Then we nd all the families of the resonant elliptic Restricted three body Problem, which bifurcate from the circular model. All these families are continued to the general three body Problem, and in this way we can obtain a global picture of all the families of periodic orbits of a two-planet resonant system. The parametric continuation, within the framework of the general Problem, takes place by varying the planetary mass ratio . We obtain bifurcations which are caused either due to collisions of the families in the space of initial conditions or due to the vanishing of bifurcation points. Our study refers to the whole range of planetary mass ratio values ( 2 (0;1)) and, therefore we include the passage from external to internal resonances. Thus we can obtain all possible stable congurations in a systematic way. Finally, we study whether the dynamics of the four known planetary systems, whose currently observed periods show a 2/1 resonance, are associated with a stable periodic orbit.
John D Hadjidemetriou - One of the best experts on this subject based on the ideXlab platform.
-
on the 2 1 resonant planetary dynamics periodic orbits and dynamical stability
Monthly Notices of the Royal Astronomical Society, 2009Co-Authors: G Voyatzis, Thomas A Kotoulas, John D HadjidemetriouAbstract:The 2/1 resonant dynamics of a two-planet planar system is studied within the framework of the three-body Problem by computing families of periodic orbits and their linear stability. The continuation of resonant periodic orbits from the Restricted to the general Problem is studied in a systematic way. Starting from the Keplerian unperturbed system we obtain the resonant families of the circular Restricted Problem. Then we nd all the families of the resonant elliptic Restricted three body Problem, which bifurcate from the circular model. All these families are continued to the general three body Problem, and in this way we can obtain a global picture of all the families of periodic orbits of a two-planet resonant system. The parametric continuation, within the framework of the general Problem, takes place by varying the planetary mass ratio . We obtain bifurcations which are caused either due to collisions of the families in the space of initial conditions or due to the vanishing of bifurcation points. Our study refers to the whole range of planetary mass ratio values ( 2 (0;1)) and, therefore we include the passage from external to internal resonances. Thus we can obtain all possible stable congurations in a systematic way. Finally, we study whether the dynamics of the four known planetary systems, whose currently observed periods show a 2/1 resonance, are associated with a stable periodic orbit.
